Reliability Prediction Basics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Reliability Prediction Basics"

Transcription

1 Reliability Prediction Basics Reliability predictions are one of the most common forms of reliability analysis. Reliability predictions predict the failure rate of components and overall system reliability. These predictions are used to evaluate design feasibility, compare design alternatives, identify potential failure areas, trade-off system design factors, and track reliability improvement. The Role of Reliability Prediction Reliability Prediction has many roles in the reliability engineering process. The impact of proposed design changes on reliability is determined by comparing the reliability predictions of the existing and proposed designs. The ability of the design to maintain an acceptable reliability level under environmental extremes can be assessed through reliability predictions. Predictions can be used to evaluate the need for environmental control systems. The effects of complexity on the probability of mission success can be evaluated by performing a reliability prediction analysis. Results from the analysis may determine a need for redundant systems, back-up systems, subsystems, assemblies, or component parts. MIL-HDBK-217 (Electronics Reliability Prediction), Bellcore/Telcordia (Electronics Reliability Prediction) and NSWC (Mechanical Reliability Prediction) provide failure rate and MTBF (Mean Time Between Failures) data for electronic and mechanical parts and equipment. A reliability prediction can also assist in evaluating the significance of reported failures. Ultimately, the results obtained by performing a reliability prediction analysis can be useful when conducting further analyses such as a FMECA (Failure Modes, Effects and Criticality Analysis), RBD (Reliability Block Diagram) or a Fault Tree analysis. The reliability predictions are used to evaluate the probabilities of failure events described in these alternate failure analysis models. Reliability and Unreliability First, let us review some concepts of reliability. At a given point in time, a component or system is either functioning or it has failed, and that the component or system operating state changes as time evolves. A working component or system will eventually fail. The failed state will continue forever, if the component or system is non-repairable. A repairable component or system will remain in the failed state for a period of time while it is being repaired and then transcends back to the functioning state when the repair is completed. This transition is assumed to be instantaneous. The change from a functioning to a failed state is failure while the change from a failure to a functioning state is referred to as repair. It is also assumed that repairs bring the component or system back to an as good as new condition. This cycle continues with the repair-tofailure and the failure-to-repair process; and then, repeats over and over for a repairable system. The reliability prediction standards such as MIL-217, Bellcore/Telcordia and NSWC Mechanical assume the component or system to be non-repairable, in a new condition at Copyright 2007, ITEM Software, Inc. Page 1 of 9

2 time zero and have a constant failure rate, if evaluated over a very long time period and using an infinite or very large sample size of components or systems. Reliability (for non-repairable items) can be defined as the probability that an item will perform a defined function without failure under stated conditions for a stated period of time. One must grasp the concept of probabilities in order to understand the concept of reliability. The numerical values of both reliability and unreliability are expressed as a probability from 0 to 1 and have no units. Reliability stated in another way: The Reliability, R(, of a component or system is defined as the probability that the component or system remains operating from time zero to time t 1, given that it was operating at time zero. Or stated another way for repairable items: The Reliability, R(, is defined as the probability that the component or system experiences no failures during the time interval zero to t 1 given that the component or system was repaired to a like new condition or was functioning at t 0. And: The Unreliability, F(, of a component or system is defined as the probability that the component or system experiences the first failure or has failed one or more times during the time interval zero to time t, given that it was operating or repaired to a like new condition at time zero. Or stated another way: The Unreliability, F(, of a component or system at a given time is simply the number of components failed to time t divided by the total number of samples tested. The following relationship holds true since a component or system must either experience its first failure in the time interval zero to t or remain operating over this period. R( + F( = 1 or Unreliability F( = 1 R( Availability and Unavailability In reliability engineering and reliability studies, it is the general convention to deal with unreliability and unavailability values rather than reliability and availability. The numerical value of both availability and unavailability are also expressed as a probability from 0 to 1 with no units. The Availability, A(, of a component or system is defined as the probability that the component or system is operating at time t, given that it was operating at time zero. Copyright 2007, ITEM Software, Inc. Page 2 of 9

3 The Unavailability, Q(, of a component or system is defined as the probability that the component or system is not operating at time t, given that is was operating at time zero. Or stated another way: Unavailability, Q( is the probability that the component or system is in the failed state at time t and is equal to the number of the failed components at time t divided by the total sample. Therefore, the following relationship holds true since a component or system must be either operating or not operating at any time: A( + Q( = 1 Both parameters are used in reliability assessments, safety and cost related studies. The following relationship holds: For a non-repairable component or system: Unavailability Q( Unreliability F( Unavailability Q( = Unreliability F( NOTE: This general equality only holds for system unavailability and unreliability if all the components within the system are non-repairable up to time t. Reliability Prediction Definitions Failure Rates Reliability predictions are based on failure rates. Conditional Failure Rate or Failure Intensity, λ(, can be defined as the anticipated number of times an item will fail in a specified time period, given that it was as good as new at time zero and is functioning at time t. It is a calculated value that provides a measure of reliability for a product. This value is normally expressed as failures per million hours (fpmh or 10 6 hours), but can also be expressed, as is the case with Bellcore/Telcordia, as failures per billion hours (fits or failures in time or 10 9 hours). For example, a component with a failure rate of 2 failures per million hours would be expected to fail 2 times in a million-hour time period. Failure rate calculations are based on complex models which include factors using specific component data such as temperature, environment, and stress. In the prediction model, assembled components are structured serially. Thus, calculated failure rates for assemblies are a sum of the individual failure rates for components within the assembly. There are three common basic categories of failure rates: Copyright 2007, ITEM Software, Inc. Page 3 of 9

4 Mean Time Between Failures (MTBF) Mean Time To Failure (MTTF) Mean Time To Repair (MTTR) Mean Time Between Failures (MTBF) Mean time between failures (MTBF) is a basic measure of reliability for repairable items. MTBF can be described as the time passed before a component, assembly, or system fails, under the condition of a constant failure rate. Another way of stating MTBF is the expected value of time between two consecutive failures, for repairable systems. It is a commonly used variable in reliability and maintainability analyses. MTBF can be calculated as the inverse of the failure rate, λ, for constant failure rate systems. For example, for a component with a failure rate of 2 failures per million hours, the MTBF would be the inverse of that failure rate, λ, or: 1 1 MTBF = OR = 500,000hours / λ 6 2Failures /10 hours failure NOTE: Although MTBF was designed for use with repairable items, it is commonly used for both repairable and non-repairable items. For non-repairable items, MTBF is the time until the first (an only) failure after t 0. Mean Time To Failure (MTTF) Mean time to failure (MTTF) is a basic measure of reliability for non-repairable systems. It is the mean time expected until the first failure of a piece of equipment. MTTF is a statistical value and is intended to be the mean over a long period of time and with a large number of units. For constant failure rate systems, MTTF is the inverse of the failure rate, λ. If failure rate, λ, is in failures/million hours, MTTF = 1,000,000 / Failure Rate, λ, for components with exponential distributions. Or 1 MTTF = 6 λ failures /10 hours For repairable systems, MTTF is the expected span of time from repair to the first or next failure. Mean Time to Repair (MTTR) Mean time to repair (MTTR) is defined as the total amount of time spent performing all corrective or preventative maintenance repairs divided by the total number of those repairs. It is the expected span of time from a failure (or shut down) to the repair or maintenance completion. This term is typically only used with repairable systems. Failure Frequencies There are four failure frequencies, which are commonly used in reliability analyses. Copyright 2007, ITEM Software, Inc. Page 4 of 9

5 Failure Density f ( - The failure density of a component or system, f (, is defined as the probability per unit time that the component or system experiences its first failure at time t, given that the component or system was operating at time zero. Failure Rate r ( - The failure rate of a component or system, r (, is defined as the probability per unit time that the component or system experiences a failure at time t, given that the component or system was operating at time zero and has survived to time t. Conditional Failure Intensity (or Conditional Failure Rate) λ ( - The conditional failure intensity of a component or system, λ (, is defined as the probability per unit time that the component or system experiences a failure at time t, given that the component or system was operating, or was repaired to be as good as new, at time zero and is operating at time t. Unconditional Failure Intensity or Failure Frequency ω ( - The unconditional failure intensity of a component or system, ω (, is defined as the probability per unit time that the component or system experiences a failure at time t, given that the component or system was operating at time zero. Relationships Between Failure Parameters The following relations exist between failure parameters. R ( + F( = 1 df( f ( = dt F( = t f ( u). du 0 f ( r( = 1 F( R 0 ( = e F t = e 0 ( ) 1 t r( u). du t f t = r t e 0 ( ) ( ) t r( u). du r( u). du Copyright 2007, ITEM Software, Inc. Page 5 of 9

6 The definitions for failure rate r ( and conditional failure intensity λ ( differ in that that the failure rate definition addresses the first failure of the component or system rather than any failure of the component or system. In the special cases of the failure rate being constant with respect to time or if the component is non-repairable these two quantities are equal. In summary : λ ( t ) =r( for non-repairable components λ ( t ) =r( for constant failure rates λ ( r( for the general case The difference between the conditional failure intensity (CFI) λ ( and unconditional failure intensity ω ( is that the CFI has an additional condition that the component or system has survived to time t. The relationship between these two quantities may be expressed mathematically as ω ( =λ( [1 Q( ] For most reliability and availability studies the unavailability Q ( of components and systems is very much less than 1. In such cases ω( λ( Constant Failure Rates If the failure rate is constant then the following expressions apply : R( = e λt F( = 1 e f ( e λt t =λ λ As can be seen from the equation above a constant failure rate results in an exponential failure density distribution. Repairable and Non-repairable Items It is important to distinguish between repairable and non-repairable items when predicting or measuring reliability. Non-repairable items Non-repairable items are components or systems such as a light bulb, transistor, rocket motor, etc. Their reliability is the survival probability over the items expected life or over a specific period of time during its life, when only one failure can occur. During the component or systems life, the instantaneous probability of the first and only failure is called the hazard rate or failure rate, r (. Life values such as MTTF described above are used to define non-repairable items. Copyright 2007, ITEM Software, Inc. Page 6 of 9

7 Repairable Items For repairable items, reliability is the probability that failure will not occur in the time period of interest; or when more than one failure can occur, reliability can be expressed as the failure rate, λ, or the rate of occurrence of failures (ROCOF). In the case of repairable items, reliability can be characterized by MTBF described above, but only under the condition of constant failure rate. There is also the concern for availability, A(, of repairable items since repair takes time. Availability, A(, is affected by the rate of occurrence of failures (failure rate, λ) or MTBF plus maintenance time; where maintenance can be corrective (repair) or preventative (to reduce the likelihood of failure). Availability, A(, is the probability that an item is in an operable state at any time Availability ( ) At = MTBF MTBF + MTTR Some systems are considered both repairable and non-repairable, such as a missile. It is repairable while under test on the ground; but becomes a non-repairable system when fired. NOTE: Failure rate, λ, is applied loosely to non-repairable items. What is really meant in a repairable system, which contains a part, is that the part will contribute to the overall system failure rate by the stated part failure rate. The part being non-repairable cannot have a failure rate. Failure Patterns (Non-repairable Items) There are three patterns of failures for non-repairable items, which can change with time. The failure rate (hazard rate) may be decreasing, increasing or constant. 1. Decreasing Failure Rate (Non-repairable Items) A decreasing failure rate (DFR) can be caused by an item, which becomes less likely to fail as the survival time increases. This is demonstrated by electronic equipment during their early life or the burn-in period. This is demonstrated by the first half of the traditional bath tub curve for electronic components or equipment where failure rate is decreasing during the early life period. 2. Constant Failure Rate (Non-repairable Items) A constant failure rate (CFR) can be caused by the application of loads at a constant average rate in excess of the design specifications or strength. These are typically externally induced failures. 3. Increasing Failure Rate (Non-repairable Items) An increasing failure rate (IFR) can be caused by material fatigue or by strength deterioration due to cyclic loading. Its failure mode does not accrue for a finite time, then exhibits an increasing probability of occurrence. Copyright 2007, ITEM Software, Inc. Page 7 of 9

8 This failure pattern is also demonstrated by electronic equipment that has aged beyond its useful life (right hand side of the bath tub curve) and the failure rate is rapidly increasing with time. Typical Bath Tub Curve Early Life or High Failure Rate Stage (Failure of Weak or Defective Components) (Burn-in Period) Wearout or Increasing Failure Rate Stage (End of Useful Life) Failure Rate r( Steady-state or Constant Failure Rate Stage Prime-of-Life (Failures Occur Randomly) Failures Age (Useful Life) Externally Induced Figure 1 Typical Bath Tub Curve Failure Patterns (Repairable Items) There are three patterns of failures for repairable items, which can change with time. The failure rate (hazard rate) may be decreasing, increasing or constant. 1. Decreasing Failure Rate (Repairable Items) An item whose reliability is improved by progressive repair and / or burn-in can cause a decreasing failure rate (DFR) pattern. 2. Constant Failure Rate (Repairable Items) A constant failure rate (CFR) is indicative of externally induced failures as in the constant failure rate of non-repairable items. This is typical of complex systems subject to repair and overhaul. 3. Increasing Failure Rate (Repairable Items) Copyright 2007, ITEM Software, Inc. Page 8 of 9

9 This increasing failure rate (IFR) pattern is demonstrated by repairable equipment when wear out modes begin to predominate or electronic equipment that has aged beyond its useful life (right hand side of the bath tub curve) and the failure rate is increasing with time. Redundancy Redundancy is briefly defined as the existence of two or more means, not necessarily identical, for accomplishing a given single function. There are different types of redundancy. Active Redundancy Has all items operating simultaneously in parallel. All items are working and in use at the same time, even though only one item is required for the function. There is no change in the failure rate of the surviving item after the failure of a companion item. Pure Parallel No Change in the failure rate of surviving items after failure of a companion item. Shared Parallel Failure rate of remaining items change after failure of a companion item. Standby Redundancy Has alternate items activated upon failure of the first item. Only one item is operating at a time to accomplish the function. One item s failure rate affects the failure characteristics of others as they are now more susceptible to failure beause they are now under load. Hot Standby Same as Active Standby or Active Redundancy. Cold Standby (Passive) Normally not operating. Do not fail when they are on cold standby. Failure of an item forces standby item to start operating. Warm Standby Normally active or operational, but not under load. Failure rate will be less due to lower stress. R-out-of-n Systems Redundant system consisting of n items in which r of the n items must function for the system to function (voting decision). Copyright 2007, ITEM Software, Inc. Page 9 of 9

The purpose of this procedure is to document the process for generating Reliability Block Diagram (RBD) for Sydney Water s facility assets.

The purpose of this procedure is to document the process for generating Reliability Block Diagram (RBD) for Sydney Water s facility assets. Procedure Reliability Block Diagram (RBD). Overview.. Objective The purpose of this procedure is to document the process for generating Reliability Block Diagram (RBD) for Sydney Water s facility assets..2.

More information

Mean Time Between Failure (MTBF)

Mean Time Between Failure (MTBF) Mean Time Between Failure (MTBF) by Vance Persons, Joseph Dykshorn Introduction MTBF stands for Mean Time Between Failures. It is a term that represents reliability of a given product. We will discuss

More information

System risks, reliability and costs

System risks, reliability and costs System risks, reliability and costs Systems always have risks attached to them. How do we deal with risks? How reliable are systems? And what do systems cost anyway? That s what we ll look at in this chapter.

More information

"Reliability and MTBF Overview"

Reliability and MTBF Overview "Reliability and MTBF Overview" Prepared by Scott Speaks Vicor Reliability Engineering Introduction Reliability is defined as the probability that a device will perform its required function under stated

More information

Reliability Workbench

Reliability Workbench Reliability Workbench RELIABILITY WORKBENCH Reliability Workbench incorporating FaultTree+ is the world leading software suite for reliability and safety analysis of systems. It is widely used in industries

More information

Design for X. Objectives of the session

Design for X. Objectives of the session Design for X Dr Jane Marshall Product Excellence using 6 Sigma Module PEUSS 2012/2013 Design for X Page 1 Objectives of the session Introduce Design for X Discuss Specific Design for X methods PEUSS 2012/2013

More information

Reliability Block Diagram RBD

Reliability Block Diagram RBD Information Technology Solutions Reliability Block Diagram RBD Assess the level of failure tolerance achieved RELIABIL ITY OPTIMIZATION System reliability analysis for sophisticated and large scale systems.

More information

MAINTAINED SYSTEMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University ENGINEERING RELIABILITY INTRODUCTION

MAINTAINED SYSTEMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University ENGINEERING RELIABILITY INTRODUCTION MAINTAINED SYSTEMS Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University OUTLINE MAINTE MAINTE MAINTAINED UNITS Maintenance can be employed in two different manners: Preventive

More information

Managing Building Services Maintenance Risk with Prediction Theories

Managing Building Services Maintenance Risk with Prediction Theories Managing Building Services Maintenance Risk with Prediction Theories K. C. Lam Dept. of Building Services Engineering The Hong Kong Polytechnic University Hong Kong Abstract When building services maintenance

More information

Chapters 3 and 4 Fault Tree Analysis

Chapters 3 and 4 Fault Tree Analysis Chapters 3 and 4 Fault Tree Analysis Marvin Rausand marvin.rausand@ntnu.no RAMS Group Department of Production and Quality Engineering NTNU (Version 0.1) Marvin Rausand (RAMS Group) System Reliability

More information

Product Excellence using 6 Sigma (PEUSS)

Product Excellence using 6 Sigma (PEUSS) Section 7 WARWICK MANUFACTURING GROUP Product Excellence using 6 Sigma (PEUSS) Introduction to Reliability AN INTRODUCTION TO RELIABILITY ENGINEERING Contents 1 Introduction 1 2 Measuring reliability 4

More information

Reliability of Technical Systems

Reliability of Technical Systems Reliability of Technical Systems Main Topics 1. Short Introduction, Reliability Parameters: Failure Rate, Failure Probability, etc. 2. Some Important Reliability Distributions 3. Component Reliability

More information

Mean Time Between Failure: Explanation and Standards

Mean Time Between Failure: Explanation and Standards Mean Time Between Failure: Explanation and Standards By Wendy Torell Victor Avelar White Paper #78 Executive Summary Mean Time Between Failure is a reliability term used loosely throughout many industries

More information

Calculating Reliability using FIT & MTTF: Arrhenius HTOL Model

Calculating Reliability using FIT & MTTF: Arrhenius HTOL Model by Paul Ellerman, Director of Reliability pellerman@microsemi.com Calculating Reliability using FIT & MTTF: Arrhenius HTOL Model Scope Establish a method for calculating the standard reliability values

More information

Using Fault Trees to Analyze Safety-Instrumented Systems

Using Fault Trees to Analyze Safety-Instrumented Systems Using Fault Trees to Analyze Safety-Instrumented Systems Joseph R. Belland Isograph, Inc., Irvine, USA Abstract: Safety-instrumented systems are protection functions frequently seen in automotive, chemical

More information

4.State dependent models

4.State dependent models 4.State dependent models 4. Markov processes Markov processes can model a system which is considered to be in any one of a discrete set of states fs ; S ; :::; S k g at time t (continuous time). The fundamental

More information

Mean Time Between Failure: Explanation and Standards

Mean Time Between Failure: Explanation and Standards Mean Time Between Failure: Explanation and Standards White Paper 78 Revision 1 by Wendy Torell and Victor Avelar > Executive summary Mean time between failure is a reliability term used loosely throughout

More information

Module 13. Software Reliability and Quality Management. Version 2 CSE IIT, Kharagpur

Module 13. Software Reliability and Quality Management. Version 2 CSE IIT, Kharagpur Module 13 Software Reliability and Quality Management Lesson 32 Software Reliability Issues Specific Instructional Objectives At the end of this lesson the student would be able to: Differentiate between

More information

Issue 1.0 Jan 2002. A Short Guide to Quality and Reliability Issues In Semiconductors For High Rel. Applications

Issue 1.0 Jan 2002. A Short Guide to Quality and Reliability Issues In Semiconductors For High Rel. Applications Issue 1.0 Jan 2002 A Short Guide to Quality and Reliability Issues In Semiconductors For High Rel. Applications It is impossible to test Quality or Reliability into a product. It is, however, quite practical

More information

MTBF, MTTR, MTTF & FIT Explanation of Terms

MTBF, MTTR, MTTF & FIT Explanation of Terms MTBF, MTTR, MTTF & FIT Explanation of Terms Purpose The intent of this White Paper is to provide an understanding of MTBF and other product reliability methods. Understanding the methods for the lifecycle

More information

Item ToolKit Technical Support Notes

Item ToolKit Technical Support Notes Item ToolKit Notes Managing Product Life Cycle in Item ToolKit 2190 Towne Centre Place Suite 314 Anaheim, CA 92806 Phone: +1.714.935.2900 Fax: +1.714.935.2911 http:// Page 1 of 9 Copyright 2006, All Rights

More information

Fault Management for System Safety: Introduction to Fault Tree Analysis

Fault Management for System Safety: Introduction to Fault Tree Analysis Fault Management for System Safety: Introduction to Fault Tree Analysis Guest Lecture SYST 460/560: Michael Scher 7 December 2009 Overview What is Fault Tree Analysis? Relevant Definitions Role of FTA

More information

CERTIFIED RELIABILITY ENGINEER (CRE) BODY OF KNOWLEDGE

CERTIFIED RELIABILITY ENGINEER (CRE) BODY OF KNOWLEDGE CERTIFIED RELIABILITY ENGINEER (CRE) BODY OF KNOWLEDGE The topics in this Body of Knowledge include additional detail in the form of subtext explanations and the cognitive level at which the questions

More information

CHAPTER 1. Introduction

CHAPTER 1. Introduction CHAPTER 1 Introduction This introductory chapter provides an overview of quality and reliability engineering techniques, the relationship between reliability and cost, and reliability, design, and assessment.

More information

Alessandro Birolini. ineerin. Theory and Practice. Fifth edition. With 140 Figures, 60 Tables, 120 Examples, and 50 Problems.

Alessandro Birolini. ineerin. Theory and Practice. Fifth edition. With 140 Figures, 60 Tables, 120 Examples, and 50 Problems. Alessandro Birolini Re ia i it En ineerin Theory and Practice Fifth edition With 140 Figures, 60 Tables, 120 Examples, and 50 Problems ~ Springer Contents 1 Basic Concepts, Quality and Reliability Assurance

More information

Advancements in LED Technology

Advancements in LED Technology Advancements in LED Technology Advancements in LED (Light Emitting Diode) technology have made this source an attractive alternative to traditional light sources in a variety of applications. One such

More information

Introduction to Basic Reliability Statistics. James Wheeler, CMRP

Introduction to Basic Reliability Statistics. James Wheeler, CMRP James Wheeler, CMRP Objectives Introduction to Basic Reliability Statistics Arithmetic Mean Standard Deviation Correlation Coefficient Estimating MTBF Type I Censoring Type II Censoring Eponential Distribution

More information

Software Reliability Introduction. Barbara Russo

Software Reliability Introduction. Barbara Russo Software Reliability Introduction Barbara Russo Lessons learned } Reliability concerns the study of failures } There are different notions of effect of an error } Often the difference regards where and

More information

DEDICATED TO EMBEDDED SOLUTIONS

DEDICATED TO EMBEDDED SOLUTIONS DEDICATED TO EMBEDDED SOLUTIONS RELIABILITY IN SUBSEA ELECTRONICS TECHNIQUES TO OBTAIN HIGH RELIABILITY STIG-HELGE LARSEN KARSTEN KLEPPE DATA RESPONS 2012-10-16 AGENDA Introduction Analysis and Design

More information

Embedded Systems Lecture 9: Reliability & Fault Tolerance. Björn Franke University of Edinburgh

Embedded Systems Lecture 9: Reliability & Fault Tolerance. Björn Franke University of Edinburgh Embedded Systems Lecture 9: Reliability & Fault Tolerance Björn Franke University of Edinburgh Overview Definitions System Reliability Fault Tolerance Sources and Detection of Errors Stage Error Sources

More information

CHAPTER 4 MONTE-CARLO SIMULATION CONTENTS

CHAPTER 4 MONTE-CARLO SIMULATION CONTENTS Applied R&M Manual for Defence Systems Part D - Supporting Theory CHAPTER 4 MONTE-CARLO SIMULATION CONTENTS Page 1 SIMULATION AND ANALYTIC MODELS 2 2 COMPARISON OF METHODS 2 3 STATISTICAL ACCURACY OF RESULTS

More information

Chapter 8: Reliability and Availability

Chapter 8: Reliability and Availability 1 Chapter 8: Reliability is critical to many modern electronic systems. Applications such as routers and wireless base stations generate revenue for the ISP or carrier for only as long as they are available.

More information

C 1 C 2 C i C n C 1 C 2. C i. C n

C 1 C 2 C i C n C 1 C 2. C i. C n Exercises 1. A microcomputer system consists of a microprocessor CPU chip and a random access memory chip. The CPU is selected from a lot of 100 of which 10 are defective and the memory chip is selected

More information

Copyright Tyco Electronics Corporation Page 1 of 7

Copyright Tyco Electronics Corporation Page 1 of 7 ABSTRACT Reliability is a term which is commonly used. But the actual meaning of reliability and the problems associated with determining it are often not understood. This paper briefly examines reliability

More information

Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview

Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview 1 (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview Prof. Dr. Liggesmeyer, 1 Content Classification Hazard and Operability Study (HAZOP) Preliminary

More information

Technical Note SolarEdge Reliability Methodology

Technical Note SolarEdge Reliability Methodology Technical Note SolarEdge Reliability Methodology Summary SolarEdge Technologies develops and sells power electronics for the Photovoltaic market. The heart of the SolarEdge power harvesting system is a

More information

Reliability Tools and Analysis Methods for Nuclear Power Plants. Sharon Honecker, PhD Research Scientist ReliaSoft Corporation Tucson, Arizona

Reliability Tools and Analysis Methods for Nuclear Power Plants. Sharon Honecker, PhD Research Scientist ReliaSoft Corporation Tucson, Arizona Reliability Tools and Analysis Methods for Nuclear Power Plants Sharon Honecker, PhD Research Scientist ReliaSoft Corporation Tucson, Arizona Overview What is reliability? What methods can help me ensure

More information

RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA

RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA RANDOM VIBRATION AN OVERVIEW by Barry Controls, Hopkinton, MA ABSTRACT Random vibration is becoming increasingly recognized as the most realistic method of simulating the dynamic environment of military

More information

Reliability of electronics: HALT-testing. 1 I. Vervenne. Outline. Reliability. Failure rate. Failure rate and reliability. Failure rate calculation

Reliability of electronics: HALT-testing. 1 I. Vervenne. Outline. Reliability. Failure rate. Failure rate and reliability. Failure rate calculation Outline Reliability of electronics: HALT-testing Isabelle Vervenne TUSofia, 9 th September 20 Reliability analysis Some definitions Failure rate of electronic components HALT (highly accelerated life tes

More information

Designing Fault-Tolerant Power Infrastructure

Designing Fault-Tolerant Power Infrastructure Designing Fault-Tolerant Power Infrastructure System Analysis and New Standards Enable Maximization of Operating Dependability for Data Centers & Other Mission Critical Facilities J.F. Christin (Author)

More information

Military Reliability Modeling William P. Fox, Steven B. Horton

Military Reliability Modeling William P. Fox, Steven B. Horton Military Reliability Modeling William P. Fox, Steven B. Horton Introduction You are an infantry rifle platoon leader. Your platoon is occupying a battle position and has been ordered to establish an observation

More information

Designed for uptime. Defining data center availability via a tier classification system

Designed for uptime. Defining data center availability via a tier classification system Defining data center availability via a tier classification system MIETEK GLIKOWSKI All systems can fail this is a simple fact that every industry must deal with. The paramount concern for the data center

More information

Reliability of Systems and Components

Reliability of Systems and Components Reliability of Systems and Components GNS Systems GmbH Am Gaußberg 2 38114 Braunschweig / Germany Fri 13 Apr 2012, Revision 0.1.1 Please send comments about this document to: norman.krebs@gns-systems.de

More information

Weibull Analysis of Truck Tyre Failures

Weibull Analysis of Truck Tyre Failures Weibull Analysis of Truck Tyre Failures Weibull Analysis has become popular as a means of identifying equipment parts failure patterns. The shape of the failure curve allows us to identify whether the

More information

A System Engineering Reliability Study of the A-10 Attack Aircraft using data

A System Engineering Reliability Study of the A-10 Attack Aircraft using data A System Engineering Reliability Study of the A-10 Attack Aircraft using 2004 2008 data The NDIA 18 th Annual System Engineering Conference October 29, 2015 Joseph Brady Dissertation Topic Department of

More information

Certified Reliability Engineer

Certified Reliability Engineer Certified Reliability Engineer Quality excellence to enhance your career and boost your organization s bottom line asq.org/certification Certification from ASQ is considered a mark of quality excellence

More information

Fault Tree Analysis. Table of Contents

Fault Tree Analysis. Table of Contents M. Pandey, University of Waterloo CIVE 240 Engineering and Sustainable Development Fault Tree Analysis Table of Contents Introduction... 3 Fault Tree Analysis... 3 Basic Events... 4 Advantages... 4 Limitations...

More information

Calculating Total System Availability

Calculating Total System Availability Calculating Total System Availability Hoda Rohani, Azad Kamali Roosta Information Services Organization KLM-Air France Amsterdam Supervised by Betty Gommans, Leon Gommans Abstract In a mission critical

More information

Reliability aspects on Power Supplies

Reliability aspects on Power Supplies Reliability aspects on Power Supplies Design Note 002 Ericsson Power Modules General Abstract As power supplies are the very heart of every electronic equipment, special attention must be paid to their

More information

Value Paper Author: Edgar C. Ramirez. Diverse redundancy used in SIS technology to achieve higher safety integrity

Value Paper Author: Edgar C. Ramirez. Diverse redundancy used in SIS technology to achieve higher safety integrity Value Paper Author: Edgar C. Ramirez Diverse redundancy used in SIS technology to achieve higher safety integrity Diverse redundancy used in SIS technology to achieve higher safety integrity Abstract SIS

More information

HALT and Reliability Workshop

HALT and Reliability Workshop HALT and Reliability Workshop Elite Electronic Engineering Steve Laya 630-495-9770 x 119, sglaya@elitetest.com HALT and Reliability Workshop Topics Covered Reliability and Planning Overview of Reliability

More information

Reliability Data Analysis

Reliability Data Analysis IAEA Training Course on Safety Assessment of NPPs to Assist Decision Making Reliability Data Analysis Lecturer Lesson Lesson IV IV 3_5 3_5 Workshop Information IAEA Workshop City, XX XX - City -XX, Country

More information

Independent analysis methods for Data Centers

Independent analysis methods for Data Centers Bilfinger HSG Facility Management GmbH Independent analysis methods for Data Centers Max Altmeyer / Marvin Köhler August 19 th, 2015 Agenda 1. Weak point analysis 2. Energy efficiency analysis 3. Combined

More information

The role of Maintenance Planning in business and its foundation basics

The role of Maintenance Planning in business and its foundation basics The role of Planning in business and its foundation basics Joe and Ted will take you through the course presentation. Hi Hello! This is Joe. This is Ted. Day 1 of the course Planning and Scheduling exists

More information

cahiers techniques 144

cahiers techniques 144 cahiers techniques 144 introduction to dependability design P. Bonnefoi Pascal Bonnefoi earned his engineering degree ESE in 1985. After working for a year in Operational Research for the French Navy he

More information

International Journal of Advances in Science and Technology (IJAST)

International Journal of Advances in Science and Technology (IJAST) Determination of Economic Production Quantity with Regard to Machine Failure Mohammadali Pirayesh 1, Mahsa Yavari 2 1,2 Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University

More information

Solving Data Loss in Massive Storage Systems Jason Resch Cleversafe

Solving Data Loss in Massive Storage Systems Jason Resch Cleversafe Solving Data Loss in Massive Storage Systems Jason Resch Cleversafe 2010 Storage Developer Conference. Insert Your Company Name. All Rights Reserved. 1 In the beginning There was replication Long before

More information

Chapter 9 Reliability Centered Maintenance

Chapter 9 Reliability Centered Maintenance Chapter 9 Reliability Centered Maintenance Marvin Rausand marvin.rausand@ntnu.no RAMS Group Department of Production and Quality Engineering NTNU (Version 0.1) Marvin Rausand (RAMS Group) System Reliability

More information

5.0 HARDWARE/SOFTWARE SYSTEM RELIABILITY MODELING

5.0 HARDWARE/SOFTWARE SYSTEM RELIABILITY MODELING 5.0 HARDWARE/SOFTWARE SYSTEM RELIABILITY MODELING Reliability modeling of combined hardware and software systems is in many ways analogous to reliability modeling of purely hardware systems. Reliability

More information

Executive Summary WHAT IS DRIVING THE PUSH FOR HIGH AVAILABILITY?

Executive Summary WHAT IS DRIVING THE PUSH FOR HIGH AVAILABILITY? MINIMIZE CUSTOMER SERVICE DISRUPTION IN YOUR CONTACT CENTER GENESYS SIP 99.999% AVAILABILITY PROVIDES QUALITY SERVICE DELIVERY AND A SUPERIOR RETURN ON INVESTMENT TABLE OF CONTENTS Executive Summary...1

More information

STAGE-GATING ACCELERATED RELIABILITY GROWTH IN AN INDUSTRIAL ENVIRONMENT. Dana Crowe and Alec Feinberg ESS? HALT? HASS? HAST?

STAGE-GATING ACCELERATED RELIABILITY GROWTH IN AN INDUSTRIAL ENVIRONMENT. Dana Crowe and Alec Feinberg ESS? HALT? HASS? HAST? -GATING ACCELERATED RELIABILITY GROWTH IN AN INDUSTRIAL ENVIRONMENT Dana Crowe and Alec Feinberg ABSTRACT In this paper, an Accelerated Reliability Growth (ARG) Stage-Gate (SG) process is described that

More information

PART 2 Interpreting Failure Rates...39 Chapter 4: Realistic Failure Rates and Prediction Confidence...41

PART 2 Interpreting Failure Rates...39 Chapter 4: Realistic Failure Rates and Prediction Confidence...41 Contents Preface...xix Acknowledgements...xxi PART 1 Understanding Reliability Parameters and Costs...1 Chapter 1: The History of Reliability and Safety Technology...3 1.1 Failure Data... 3 1.2 Hazardous

More information

Reliability of Technical Systems

Reliability of Technical Systems Main Topics 1. Short Introduction, Reliability Parameters: Failure Rate, Failure Probability, etc. 2. Some Important Reliability Distributions 3. Component Reliability 4. Introduction, Key Terms, Framing

More information

Monte Carlo Simulation using Excel for Predicting Reliability of a Geothermal Plant

Monte Carlo Simulation using Excel for Predicting Reliability of a Geothermal Plant Monte Carlo Simulation using Excel for Predicting Reliability of a Geothermal Plant Daniela E. Popescu, Corneliu Popescu, Gianina Gabor University of Oradea, Str. Armatei Romane nr.5, Oradea, România depopescu@uoradea.ro,

More information

Public Goods : (b) Efficient Provision of Public Goods. Efficiency and Private Goods

Public Goods : (b) Efficient Provision of Public Goods. Efficiency and Private Goods Public Goods : (b) Efficient Provision of Public Goods Efficiency and Private Goods Suppose that there are only two goods consumed in an economy, and that they are both pure private goods. Suppose as well

More information

The Secondary Impact of System Optimisation on Building Equipment; Maintenance and Life Expectancy

The Secondary Impact of System Optimisation on Building Equipment; Maintenance and Life Expectancy ENVIRONMENTAL GROUP The Secondary Impact of System Optimisation on Building Equipment; Maintenance and Life Expectancy Dr. Houman Tamaddon JUNE 2015 INTRODUCTION The increased pace of global energy consumption

More information

GUIDANCE FOR ASSESSING THE LIKELIHOOD THAT A SYSTEM WILL DEMONSTRATE ITS RELIABILITY REQUIREMENT DURING INITIAL OPERATIONAL TEST.

GUIDANCE FOR ASSESSING THE LIKELIHOOD THAT A SYSTEM WILL DEMONSTRATE ITS RELIABILITY REQUIREMENT DURING INITIAL OPERATIONAL TEST. GUIDANCE FOR ASSESSING THE LIKELIHOOD THAT A SYSTEM WILL DEMONSTRATE ITS RELIABILITY REQUIREMENT DURING INITIAL OPERATIONAL TEST. 1. INTRODUCTION Purpose The purpose of this white paper is to provide guidance

More information

Failure Modes, Effects and Diagnostic Analysis

Failure Modes, Effects and Diagnostic Analysis Failure Modes, Effects and Diagnostic Analysis Project: Plant-STOP 9475 Company: R. STAHL Schaltgeräte GmbH Waldenburg Germany Contract No.: STAHL 13/04-027 Report No.: STAHL 13/04-027 R024 Version V1,

More information

Electric Currents. Electric Potential Energy 11/23/16. Topic 5.1 Electric potential difference, current and resistance

Electric Currents. Electric Potential Energy 11/23/16. Topic 5.1 Electric potential difference, current and resistance Electric Currents Topic 5.1 Electric potential difference, current and resistance Electric Potential Energy l If you want to move a charge closer to a charged sphere you have to push against the repulsive

More information

Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606

Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606 Report on the Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606 This report presents the results of phenol diffusivity, specific heat and calculated thermal

More information

Introduction to Software Reliability Estimation

Introduction to Software Reliability Estimation Introduction to Software Reliability Estimation 1 Motivations Software is an essential component of many safetycritical systems These systems depend on the reliable operation of software components How

More information

Comparing the Reliability of Ethernet Network Topologies in Substation Control and Monitoring Networks

Comparing the Reliability of Ethernet Network Topologies in Substation Control and Monitoring Networks Comparing the Reliability of Ethernet Network Topologies in Substation Control and Monitoring Networks Gary W. Scheer and David J. Dolezilek Schweitzer Engineering Laboratories, Inc. Presented at UTC Telecom

More information

Basics of Traditional Reliability

Basics of Traditional Reliability Basics of Traditional Reliability Where we are going Basic Definitions Life and ties of a Fault Reliability Models N-Modular redundant systes Definitions RELIABILITY: SURVIVAL PROBABILITY When repair is

More information

Rajkumar B. Patil 1, L. Y. Waghmode 2, P. B. Chikali 3, T. S. Mulla 4.

Rajkumar B. Patil 1, L. Y. Waghmode 2, P. B. Chikali 3, T. S. Mulla 4. IOSR Journal of Mechanical & Civil Engineering (IOSR-JMCE) ISSN: 2278-1684, PP: 14-18 www.iosrjournals.org An Overview of Fault Tree Analysis (FTA) Method for Reliability Analysis & Life Cycle Cost (LCC)

More information

Calculation of Semiconductor Failure Rates

Calculation of Semiconductor Failure Rates Calculation of Semiconductor Failure Rates William J. Vigrass One of the fundamentals of understanding a product s reliability requires an understanding of the calculation of the failure rate. The traditional

More information

FMEA and FTA Vít Hampl

FMEA and FTA Vít Hampl FMEA and FTA Vít Hampl FMEA - Failure mode and effects analysis FMEA is a bottom-up technique used to identify, prioritize, and eliminate potential failures from the system, design or process before they

More information

SIL Safety Manual. OXYMAT 6 Gas Analyzer for the Determination of Oxygen. Supplement to instruction manual ULTRAMAT 6 and OXYMAT 6

SIL Safety Manual. OXYMAT 6 Gas Analyzer for the Determination of Oxygen. Supplement to instruction manual ULTRAMAT 6 and OXYMAT 6 OXYMAT 6 Gas Analyzer for the Determination of Oxygen SIL Safety Manual Supplement to instruction manual ULTRAMAT 6 and OXYMAT 6 OXYMAT 6F 7MB2011, 7MB2017 OXYMAT 6E 7MB2021, 7MB2027 ULTRAMAT/OXYMAT 6E

More information

CHAPTER 29 FAULT / SUCCESS TREE ANALYSIS CONTENTS

CHAPTER 29 FAULT / SUCCESS TREE ANALYSIS CONTENTS Applied R&M Manual for Defence Systems Part C - Techniques CHAPTER 29 FAULT / SUCCESS TREE ANALYSIS CONTENTS Page 1 Introduction 2 2 Definitions 3 3 Features and Analysis 3 4 Construction 4 5 Analysis

More information

FAULT TREE ANALYSIS REPORT FOR THE AUTOMATIC BRAKE SYSTEM. Prepared by

FAULT TREE ANALYSIS REPORT FOR THE AUTOMATIC BRAKE SYSTEM. Prepared by FAULT TREE ANALYSIS REPORT FOR THE AUTOMATIC BRAKE SYSTEM Prepared by Sample Company 111 Foothill Blvd. Suite E-156 La Canada Flintridge, California 91011 July 2002 Copyright 2002 by Probabilistic Software,

More information

Reliability. 26.1 Reliability Models. Chapter 26 Page 1

Reliability. 26.1 Reliability Models. Chapter 26 Page 1 Chapter 26 Page 1 Reliability Although the technological achievements of the last 50 years can hardly be disputed, there is one weakness in all mankind's devices. That is the possibility of failure. What

More information

Avoiding AC Capacitor Failures in Large UPS Systems

Avoiding AC Capacitor Failures in Large UPS Systems Avoiding AC Capacitor Failures in Large UPS Systems White Paper #60 Revision 0 Executive Summary Most AC power capacitor failures experienced in large UPS systems are avoidable. Capacitor failures can

More information

PHYSICS EXPERIMENTS (HEAT)

PHYSICS EXPERIMENTS (HEAT) PHYSICS EXPERIMENTS (HEAT) In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than

More information

5 Aleatory Variability and Epistemic Uncertainty

5 Aleatory Variability and Epistemic Uncertainty 5 Aleatory Variability and Epistemic Uncertainty Aleatory variability and epistemic uncertainty are terms used in seismic hazard analysis that are not commonly used in other fields, but the concepts are

More information

CEM 515: Project Quality Management

CEM 515: Project Quality Management King Fahd University of Petroleum & Minerals Department of Construction Engineering & Management CEM 515: Project Quality Management SIX SIGMA FOR PROJECT MANAGERS GROUP# 1 Monday, December 11, 2006 OUTLINE

More information

Generic Reliability Evaluation Method for Industrial Grids with Variable Frequency Drives

Generic Reliability Evaluation Method for Industrial Grids with Variable Frequency Drives Energy and Power Engineering, 2013, 5, 83-88 doi:10.4236/epe.2013.54b016 Published Online July 2013 (http://www.scirp.org/journal/epe) Generic Reliability Evaluation Method for Industrial Grids with Variable

More information

Availability Assessment of Generating Units of Balimela Hydro Electric Power Station (510 MW) A Markovian Approach

Availability Assessment of Generating Units of Balimela Hydro Electric Power Station (510 MW) A Markovian Approach American Journal of Engineering Research (AJER) 24 American Journal of Engineering Research (AJER) e-issn : 232-847 p-issn : 232-936 Volume-3, Issue-2, pp-44-49 www.ajer.org Research Paper Open Access

More information

5.3. The Poisson distribution. Introduction. Prerequisites. Learning Outcomes. Learning Style

5.3. The Poisson distribution. Introduction. Prerequisites. Learning Outcomes. Learning Style The Poisson distribution 5.3 Introduction In this block we introduce a probability model which can be used when the outcome of an experiment is a random variable taking on positive integer values and where

More information

Advanced Fault Tree Analysis for Improved Quality and Risk Assessment

Advanced Fault Tree Analysis for Improved Quality and Risk Assessment Advanced Fault Tree Analysis for Improved Quality and Risk Assessment Jussi-Pekka Penttinen 1, Timo Lehtinen 2 Abstract Traditional fault tree analysis (FTA) has formed a common language for the modelling

More information

CEMEP UPS. The high environmental performance solution for power supply to high-availability data centers

CEMEP UPS. The high environmental performance solution for power supply to high-availability data centers CEMEP UPS The high environmental performance solution for power supply to high-availability data centers Exchanges of information and communication needs are growing at an exponential rate. That growth

More information

CHAPTER 15 SOFTWARE R&M ANALYSES CONTENTS

CHAPTER 15 SOFTWARE R&M ANALYSES CONTENTS Applied R&M Manual for Defence Systems Part B R&M Related Activities CHAPTER 15 SOFTWARE R&M ANALYSES CONTENTS Page 1 Introduction 2 2 Abbreviations 2 3 Software 3 4 Software Application R&M Techniques

More information

Cloud Computing Disaster Recovery (DR)

Cloud Computing Disaster Recovery (DR) Cloud Computing Disaster Recovery (DR) Dr. Sanjay P. Ahuja, Ph.D. 2010-14 FIS Distinguished Professor of Computer Science School of Computing, UNF Need for Disaster Recovery (DR) What happens when you

More information

Reliability in Electronics

Reliability in Electronics Technical Article Reliability in Electronics CONTENTS Introduction 1.1 Failure Rate 1.2 Reliability 1.3 Mean Time Between Failures (MTBF) Mean Time to Failure (MTTF) 1.4 Service Life (Mission Life, Life)

More information

BAYES' THEOREM IN DECISION MAKING Reasoning from Effect to Cause

BAYES' THEOREM IN DECISION MAKING Reasoning from Effect to Cause BAYES' THEOREM IN DECISION MAKING Reasoning from Effect to Cause by Jack V. Michaels, PE, CVS Value Engineering Department Martin Marietta Orlando Aerospace ABSTRACT Thomas Bayes (1702-1761) was an English

More information

Continuous Random Variables and Probability Distributions. Stat 4570/5570 Material from Devore s book (Ed 8) Chapter 4 - and Cengage

Continuous Random Variables and Probability Distributions. Stat 4570/5570 Material from Devore s book (Ed 8) Chapter 4 - and Cengage 4 Continuous Random Variables and Probability Distributions Stat 4570/5570 Material from Devore s book (Ed 8) Chapter 4 - and Cengage Continuous r.v. A random variable X is continuous if possible values

More information

SOFTWARE ENGINEERING

SOFTWARE ENGINEERING SOFTWARE ENGINEERING Chapter 26 Quality Management ETAM MEMBERS RN N 3521010116 Murali T 3521010117 Muralitharan S 3521010118 Narasimhan K 3521010119 Navaneethakrishnan D Areas Covered What is software

More information

MASTER S THESIS. Faculty of Science and Technology. Study program/ Specialization: Spring semester, Risikostyring Offshoresikkerhet

MASTER S THESIS. Faculty of Science and Technology. Study program/ Specialization: Spring semester, Risikostyring Offshoresikkerhet Faculty of Science and Technology MASTER S THESIS Study program/ Specialization: Risikostyring Offshoresikkerhet Spring semester, 2012 Open / Restricted access Writer: Monphen Toungsetwut Faculty supervisor:

More information

Maximizing UPS Availability

Maximizing UPS Availability Maximizing UPS Availability A comparative assessment of UPS designs and deployment configurations for the highavailability data center By Chris Loeffler Product Manager, BladeUPS & Data Center Applications

More information

Reliability of Data Storage Systems

Reliability of Data Storage Systems Zurich Research Laboratory Ilias Iliadis April 2, 25 Keynote NexComm 25 www.zurich.ibm.com 25 IBM Corporation Long-term Storage of Increasing Amount of Information An increasing amount of information is

More information

Fatigue Life Estimates Using Goodman Diagrams

Fatigue Life Estimates Using Goodman Diagrams Fatigue Life Estimates Using Goodman Diagrams by Robert Stone The purpose of this paper is to review the proper methods by which spring manufacturers should estimate the fatigue life of a helical compression

More information

Note 5.1 Stress range histories and Rain Flow counting

Note 5.1 Stress range histories and Rain Flow counting June 2009/ John Wægter Note 5.1 Stress range histories and Rain Flow counting Introduction...2 Stress range histories...3 General...3 Characterization of irregular fatigue loading...4 Stress range histogram...5

More information